A Spectral Collocation Solution for In-Plane Eigenvalue Analysis of Skew Plates

Free in-plane vibration analysis of isotropic plates with skew geometry is carried out using the spectral collocation method. The mathematical formulation of the discretized spectral solution is expressed in a concise matrix form which can be directly and easily coded in modern mathematical software packages. A rather comprehensive set of plate cases with various skew angles, aspect ratios, and boundary conditions is presented, with the aim of both showing the rate of convergence and degree of accuracy of the adopted method and providing useful design guidelines related to the effect of the plate geometrical parameters on the fundamental in-plane frequency value.